Cremona's table of elliptic curves

64 = 2⁶

Field	Data	Notes
Atkin-Lehner	2-	Signs for the Atkin-Lehner involutions
Class	64a	Isogeny class
Conductor	64	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	32768 = 215	Discriminant
Eigenvalues	2-  0  2  0  0 -6  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-44,112]	[a1,a2,a3,a4,a6]
j	287496	j-invariant
L	0.92703733865069	L(r)(E,1)/r!
Ω	3.7081493546027	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	64a2 32a4 576h3 1600o4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 64a3

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	0	2	0	0	-6	2	0	0	10	0	2	10	0	0	-14	0	10	0	0	-6	0	0	10	18

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Quadratic twists for elliptic curve 64a3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43
64a2	32a4	576h3	1600o4	3136t3	7744t3	10816bb4	18496i4	23104bo3	33856ba3	53824r3	61504bn3	87616z4	107584h4	118336bd3

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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